2010•Unpublished venueOpen access

Further exploration on relationship between crisp sets and fuzzy sets

Zhaoxia Wang, Quan Wang, Ming Bai, Zengqiang Chen, Zhen Sun

Abstract

This paper employs the concept of fuzzify upgrade operator to describe the relationship between crisp sets, fuzzy sets and higher order fuzzy sets, such as type-2 fuzzy sets. Theory analysis and case studies demonstrate that a crisp set can be represented by a type-1 fuzzy set, a type-1 fuzzy set can be represented by a type-2 fuzzy set, and a type-n (n>=2) fuzzy set can be represented by a type-(n+1) (n>=2) fuzzy set. The fuzzify upgrade operator makes crisp sets, type-1 fuzzy sets, type-2 fuzzy sets and any fuzzy sets much more accessible to all readers. The relationship between crisp sets and fuzzy sets are explored.

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Key concepts: Mathematics, Fuzzy set, Fuzzy set operations, Type-2 fuzzy sets and systems, Fuzzy classification, Defuzzification, Fuzzy number, Fuzzy logic